Find the `V_(ab)` in an electric field `E=(2hati+3hatj+4hatk)N/C`, where `r_a=(hati-2hatj+hatk)m` and `r_b=(2hati+hatj-2hatk)m`

Options

A. `-1 V`
B. `-2 V`
C. `1 V`
D. `2 V`

Answer

A

Explanation

Here the given field is uniform (constant) so Using
`dV=-E.dx`
`or V_(ab)=V_a-V_b=-int_b^aE.dr`
`=-int_((2,1,-2))^((1,-2,1))(2hati+3hatj+4hatk).(dxhati+dyhatj+dzhatk)`
`-int_((2,1,-2))^((1,-2,1))(2 dx+3dy+4dz)`
`-[2x+3y+4z]_((2,1,-2))^((1,-2,1))`
`=-1V`